012-the narrow bridge universe

1 .The Narrow Bridge Universe Marek Perkowski February 4, 2011

2 .Can we create a world with no evil? Most of games are based on killing enemy (chess, checkers) We propose a game to win by cooperation to save lives in a Universe with limited resources . This is my initial design of the game and you are all welcome to extend, improve and program it. This will be an application of CTL logic, the same logic as used by Terrance and Lawrance and industrial companies to verify hardware.

3 .The Narrow Bridge Problem There are two kinds of people, Meaties and Vegies . Meaties can eat only meat, Vegies can eat only vegetables. Meaties live in North, Vegies live in South. There is no meat in North. There is abundance of meat in South There is no vegetables in South There is abundance of vegetables in North. To move to North Vegies have to go through narrow bridge To move to South Meaties have to go through the same bridge. If there are two humans in the same cell (place ) on the bridge, then they must shoot . Otherwise they may not. If there are two humans in neighbor cells they may shoot or not. The human ( Meatie or Vegie ) can either kill a human in the same place, do nothing or go to other location. Meaties are obedient to General_Meat Vegies are obedient to General_Vegie If both armies do nothing, they will all die from starvation. Some life sacrifice may be necessary to save more lives. Worth of my soldier is worthy 1 to general, life of one enemy soldier is worth ½ to him What is the best strategy that will save the maximum of human lives?

4 .Example of solution

5 .Four Meaties in North Four Vegies in South Mutual kill Mutual kill

6 .Meaties undrestand to not attack Vegie undrestands to not attack

7 .Ultimately two Meaties and two Vegies survive

8 .As a result of some (evolved, agreed and thought out) late agreement, two Meaties and two Vegies will survive. Can we find a scenario in which more humans will survive?

9 .Are the rules of this Universe such that the best one can do is to sacrifice 4+4 – (2+2) = 4 people? Can we sacrifice less?

10 .Self-Sacrifice Observe that one of strategies to have the minimum death is the general sacrifice at the very beginning three of his soldiers. He gives hint to the “enemy” that he is not willing to fight for the sake of fighting, just to fight as a necessity for survival.

11 .Four Meaties in North Four Vegies in South Self-sacrifice Self-sacrifice Self-sacrifice

12 .With maximum sacrifice of Meaties a total of five lives were saved

13 .Problems to solve Program this world in nuSMV If we change slightly the rules of the game or the geometry of the universe’s land, can we save more lives? How to design the game so that no lives will be saved? How to design the game so that only one life will be lost? How can we design the game that only self-sacrifice will be the best solution?